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A class of multiphase traffic theories for microscopic, kinetic and continuum traffic models
 Comp. Math. Appl
, 2012
"... Abstract. In the present paper a review and numerical comparison of a special class of multiphase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multivalued fundamental diagrams are derived from different microscopic and ..."
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Abstract. In the present paper a review and numerical comparison of a special class of multiphase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multivalued fundamental diagrams are derived from different microscopic and kinetic models. Numerical experiments show similarities and differences of the models, in particular, for the appearance and structure of stop and go waves for highway traffic in dense situations. For all models, but one, phase transitions can appear near bottlenecks depending on the local density and velocity of the flow. 1.
AttributionNonCommercialNo Derivative Works iii Contents Preface............................ v
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The Supply Chain Triangle: How Synchronisation, Stability, and Productivity of Material Flows Interact
"... Empirical evidence created a commonly accepted understanding that synchronisation and stability of material flows impact its productivity. This crucial link between synchronous and stable material flows by time and quantity to create a supply chain with the highest throughput rates is at the heart ..."
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Empirical evidence created a commonly accepted understanding that synchronisation and stability of material flows impact its productivity. This crucial link between synchronous and stable material flows by time and quantity to create a supply chain with the highest throughput rates is at the heart of lean thinking. Although this supply chain triangle has generally been acknowledged over many years, it is necessary to reach a finer understanding of these dynamics. Therefore, we will develop and study supply chains with the help of fluid dynamics. A multistage, continuous material flow is modelled through a conservation law for material density. Unlike similar approaches, our model is not based on some quasi steadystate assumptions about the stochastic behaviour of the involved supply chain but rather on a simple deterministic rule for material flow density. These models allow us to take into account the nonlinear, dynamical interactions of different supply chain echelons and to test synchronised and stable flow with respect to its potential impacts. Numerical simulations verify that the model is able to simulate transient supply chain phenomena. Moreover, a quantification method relating to the fundamental link between synchronisation, stability, and productivity of supply chains has been found.
Research Themes on Traffic Flow on Networks
, 2013
"... Models of traffic flow can be of two main types [1, 8, 11]. 1 Microscopic particle models, describing the position and velocity of each single car. If there are N cars on a road, one thus needs to write a system of N differential equations, one for each car. These ODEs specify how each driver adjus ..."
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Models of traffic flow can be of two main types [1, 8, 11]. 1 Microscopic particle models, describing the position and velocity of each single car. If there are N cars on a road, one thus needs to write a system of N differential equations, one for each car. These ODEs specify how each driver adjusts his velocity depending on the distance and the velocity of the vehicle ahead. 2 Macroscopic models, describing the evolution of the vehicle density (i.e. the number of cars per unit length of the road). Since the total number of cars is conserved, these models consist of one or more PDEs, usually in the form of a conservation law. Particle models are easier to simulate numerically. On the other hand, macroscopic models are mathematically more interesting and yield a better qualitative understanding of traffic patterns. Having written down a set of mathematical equations, the next steps of a mathematical analysis (i) The first and most fundamental concern is making sure that the model “well posed”. This means that, given any initial configuration, the equations determine a unique solution
Prediction Based Routing for Vehicular Ad Hoc Networks
"... Development in short range wireless LAN (WLAN) and long range wireless WAN (WWAN) technologies have motivated recent efforts to integrate the two. This creates new application scenarios that were not possible before. Vehicles with only WLAN radios can use other vehicles that have both WLAN and WWAN ..."
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Development in short range wireless LAN (WLAN) and long range wireless WAN (WWAN) technologies have motivated recent efforts to integrate the two. This creates new application scenarios that were not possible before. Vehicles with only WLAN radios can use other vehicles that have both WLAN and WWAN radios as mobile gateways and connect to the Internet while on the road. The most difficult challenge in the scenario is to deal with frequent route breakages due to dynamic mobility of vehicles on the road. Existing routing protocols which are widely used for mobile ad hoc networks are reactive in nature and wait till existing routes break before constructing new routes. The frequent route failures result in significant amount of time needed for repairing existing routes or reconstructing new routes. In spite of the dynamic mobility, the motion of vehicles on highways is quite predictable compared to other mobility patterns for wireless ad hoc networks, with location and velocity information readily available. This can be exploited to predict how long a route will last between a vehicle requiring Internet connectivity and the gateway which provides a route to the Internet. Successful prediction of route lifetimes can significantly reduce the number of route failures. In this paper we introduce a prediction based routing (PBR) protocol that is specifically tailored to the mobile gateway scenario and takes advantage of the predictable mobility pattern of vehicles on highways. The protocol uses predicted route lifetimes to preemptively create new routes before existing ones fail. We study the performance of this protocol through simulation and demonstrate significant reductions in route failures compared to protocols that do not use preemptive routing. Moreover, we find that the overhead of preemptive routing is kept in check due to the ability of PBR to predict route lifetimes.
states of lattice Boltzmann models
, 2010
"... A multilevel algorithm to compute ..."
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Fundamental diagrams in traffic flow: the case of heterogeneous kinetic models
"... Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the socalled fundamental and speed diagrams) show some peculiarities not yet fully reproduced nor explained by mathematical models ..."
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Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the socalled fundamental and speed diagrams) show some peculiarities not yet fully reproduced nor explained by mathematical models. In this paper, resting on the methods of the kinetic theory, we introduce a new traffic model which takes into account the heterogeneous nature of the flow of vehicles along a road. In more detail, the model considers traffic as a mixture of two populations of vehicles (e.g., cars and trucks) with different characteristics, in particular different length and maximum speed. With this approach we gain some insights into the scattering of the data in the regime of congested traffic clearly shown by actual measurements.